OPEN-SOURCE SCRIPT
Polynomial Regression Extrapolation [LuxAlgo]

This indicator fits a polynomial with a user set degree to the price using least squares and then extrapolates the result.
Settings
Usage
Polynomial regression is commonly used when a relationship between two variables can be described by a polynomial.
In technical analysis polynomial regression is commonly used to estimate underlying trends in the price as well as obtaining support/resistances. One common example being the linear regression which can be described as polynomial regression of degree 1.
Using polynomial regression for extrapolation can be considered when we assume that the underlying trend of a certain asset follows polynomial of a certain degree and that this assumption hold true for time t+1...,t+n. This is rarely the case but it can be of interest to certain users performing longer term analysis of assets such as Bitcoin.
The selection of the polynomial degree can be done considering the underlying trend of the observations we are trying to fit. In practice, it is rare to go over a degree of 3, as higher degree would tend to highlight more noisy variations.

Using a polynomial of degree 1 will return a line, and as such can be considered when the underlying trend is linear, but one could improve the fit by using an higher degree.

The chart above fits a polynomial of degree 2, this can be used to model more parabolic observations. We can see in the chart above that this improves the fit.

In the chart above a polynomial of degree 6 is used, we can see how more variations are highlighted. The extrapolation of higher degree polynomials can eventually highlight future turning points due to the nature of the polynomial, however there are no guarantee that these will reflect exact future reversals.
Details
A polynomial regression model y(t) of degree p is described by:
Pine Script®
The vector coefficients β are obtained such that the sum of squared error between the observations and y(t) is minimized. This can be achieved through specific iterative algorithms or directly by solving the system of equations:
Pine Script®
Settings
- Length: Number of most recent price observations used to fit the model.
- Extrapolate: Extrapolation horizon
- Degree: Degree of the fitted polynomial
- Src: Input source
- Lock Fit: By default the fit and extrapolated result will readjust to any new price observation, enabling this setting allow the model to ignore new price observations, and extend the extrapolation to the most recent bar.
Usage
Polynomial regression is commonly used when a relationship between two variables can be described by a polynomial.
In technical analysis polynomial regression is commonly used to estimate underlying trends in the price as well as obtaining support/resistances. One common example being the linear regression which can be described as polynomial regression of degree 1.
Using polynomial regression for extrapolation can be considered when we assume that the underlying trend of a certain asset follows polynomial of a certain degree and that this assumption hold true for time t+1...,t+n. This is rarely the case but it can be of interest to certain users performing longer term analysis of assets such as Bitcoin.
The selection of the polynomial degree can be done considering the underlying trend of the observations we are trying to fit. In practice, it is rare to go over a degree of 3, as higher degree would tend to highlight more noisy variations.
Using a polynomial of degree 1 will return a line, and as such can be considered when the underlying trend is linear, but one could improve the fit by using an higher degree.
The chart above fits a polynomial of degree 2, this can be used to model more parabolic observations. We can see in the chart above that this improves the fit.
In the chart above a polynomial of degree 6 is used, we can see how more variations are highlighted. The extrapolation of higher degree polynomials can eventually highlight future turning points due to the nature of the polynomial, however there are no guarantee that these will reflect exact future reversals.
Details
A polynomial regression model y(t) of degree p is described by:
y(t) = β(0) + β(1)x(t) + β(2)x(t)^2 + ... + β(p)x(t)^p
The vector coefficients β are obtained such that the sum of squared error between the observations and y(t) is minimized. This can be achieved through specific iterative algorithms or directly by solving the system of equations:
β(0) + β(1)x(0) + β(2)x(0)^2 + ... + β(p)x(0)^p = y(0)
β(0) + β(1)x(1) + β(2)x(1)^2 + ... + β(p)x(1)^p = y(1)
...
β(0) + β(1)x(t-1) + β(2)x(t-1)^2 + ... + β(p)x(t-1)^p = y(t-1)
Note that solving this system of equations for higher degrees p with high x values can drastically affect the accuracy of the results. One method to circumvent this can be to subtract x by its mean.
Informacje o Wersji
Minor changes.Skrypt open-source
W duchu TradingView twórca tego skryptu udostępnił go jako open-source, aby traderzy mogli analizować i weryfikować jego funkcjonalność. Brawo dla autora! Możesz korzystać z niego za darmo, ale pamiętaj, że ponowna publikacja kodu podlega naszym Zasadom Społeczności.
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All content provided by LuxAlgo is for informational & educational purposes only. Past performance does not guarantee future results.
Join our 150k+ community: discord.gg/lux
All content provided by LuxAlgo is for informational & educational purposes only. Past performance does not guarantee future results.
Wyłączenie odpowiedzialności
Informacje i publikacje przygotowane przez TradingView lub jego użytkowników, prezentowane na tej stronie, nie stanowią rekomendacji ani porad handlowych, inwestycyjnych i finansowych i nie powinny być w ten sposób traktowane ani wykorzystywane. Więcej informacji na ten temat znajdziesz w naszym Regulaminie.
Skrypt open-source
W duchu TradingView twórca tego skryptu udostępnił go jako open-source, aby traderzy mogli analizować i weryfikować jego funkcjonalność. Brawo dla autora! Możesz korzystać z niego za darmo, ale pamiętaj, że ponowna publikacja kodu podlega naszym Zasadom Społeczności.
Get access to our exclusive tools: luxalgo.com
Join our 150k+ community: discord.gg/lux
All content provided by LuxAlgo is for informational & educational purposes only. Past performance does not guarantee future results.
Join our 150k+ community: discord.gg/lux
All content provided by LuxAlgo is for informational & educational purposes only. Past performance does not guarantee future results.
Wyłączenie odpowiedzialności
Informacje i publikacje przygotowane przez TradingView lub jego użytkowników, prezentowane na tej stronie, nie stanowią rekomendacji ani porad handlowych, inwestycyjnych i finansowych i nie powinny być w ten sposób traktowane ani wykorzystywane. Więcej informacji na ten temat znajdziesz w naszym Regulaminie.